Making Prime Numbers Click with Area Models and a 100 Chart

Prime numbers can feel abstract for students, but this week my class had an “aha!” moment that made them come alive. The key? Simple manipulatives, graph paper, and a 100 chart.

Starting with Hands-On Rectangles

I handed each partnership graph paper, crayons, and 25 unit cubes. Their first challenge:

“Take 6 cubes and see how many rectangles you can make that lay flat on the table.”

Some kids quickly found 1 × 6, but then I nudged them: “Can you make any more?” Soon, someone discovered 2 × 3.

I projected graph paper on the board and drew out the rectangles so we could all see. Then I had them repeat with 7 cubes. This time there was only one option: a long 1 × 7 rectangle.

That was our perfect lead-in:

• Composite numbers can be arranged into multiple rectangles (multiple factor pairs).
• Prime numbers only make that “long” rectangle.

Partner Exploration

Next, I set them loose:

• Each pair started with 2 cubes and worked their way up.
• Their mission? See how far they could go in 10 minutes and record their rectangles.

For my higher flyers, I tossed in a challenge: “What about 20? How many rectangles can you build?”

This naturally connected to the idea that the rectangle side lengths were the factors of the number.

The 100 Chart Sieve

Once they had that foundation, we shifted to the Sieve of Eratosthenes using a 100 chart:

1. Skip 1 because 1 is neither prime nor composite.
2. Circle 2, cross out its multiples.
3. Circle 3, skip count by 3s and cross them out.
4. Do the same with 5 and 7.

By the end, students could see that the “survivors” on the chart were the prime numbers under 100. It was visual, satisfying, and they caught on quickly.

Practice and Play

To practice identifying prime vs. composite:

• We used IXL prime/composite skills (great for quick checks).
• Then we closed with a game of Fruit Splat — a fun online review where students shouted answers across the room.

One student even said, “I get it now!” — music to a teacher’s ears.

Why It Worked

• Manipulatives first: Building numbers with cubes and rectangles grounded the abstract in something students could see and touch.
• Visual anchor: The projected graph paper and student work made their thinking visible.
• Layered practice: From manipulatives → 100 chart → digital review, each step reinforced the concept.

I’m challenging myself to use more manipulatives this year, and already I can see how much deeper the learning goes.

Action Steps

1. Try this in your classroom: Grab some cubes, print a 100 chart, and let your students build their way into understanding primes and composites.
2. Take it further: If you loved this activity but want to push your students into more rigorous, real-world problem solving, grab my free G.R.I.T. sample. It’s designed to walk students step-by-step through challenging word problems using the G.R.I.T. process (Gather, Represent, Investigate, Tie it all together).
   • 👉Get your free G.R.I.T. sample here!